Investigators at Traunsee lake in Austria where the bodies were found.

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Both the man and woman were 50-70 years old

The woman's head was encased in concrete

CNN  — 

Police in Austria appear to have a bizarre murder-suicide case on their hands.

Authorities believe a man killed a woman and then dismembered her before encasing her head in concrete. His body was found submerged in a lake.

The gruesome details began to unfold over the weekend when a suitcase with the woman’s body parts was found in Traunsee lake, about 50 miles (80 kilometers) east of Salzburg, said prosecutor Birgit Ahamer. A police dog later found a second suitcase with more pieces of her body.

The man’s body was found by divers in the lake on Monday. Attached to his hands with zip ties were two suitcases filled with rocks. The woman’s head was discovered nearby.

Investigators say the conditions of the bodies and circumstances surrounding the case lead them to believe it was a murder-suicide.

“That the woman was strangled seems … quite certain,” Ahamer said. “Because of the fact that we have found no traces of violence on the male body – and he drowned – so it seems that it was a suicide.

Authorities believe they died sometime between December 24 and January 3. Both were 50 to 70 years old.

Their identities weren’t immediately known.